Re: Expected Value

jay wrote:
On Jun 7, 11:20 am, DanCT <danmye...@xxxxxxxxxxx> wrote:
On Jun 6, 11:15 am, jay <jayesh.srivast...@xxxxxxxxx> wrote:

On Jun 6, 10:51 am, DanCT <danmye...@xxxxxxxxxxx> wrote:

I would like to compute the expectation of a continuous quantity X
where:
X = X(x) if T = 1, for T a binary value
X = 0 otherwise

X(x) will be fit using regression. The tricky part here is that T
is not known when scoring a population, so I am thinking I'll need
to resort to predicting a probability for T(t) = 1 using a logit
model.

So how do I compute E(X) in this case?

E(X) = p*E(X) where p is Pr(T = 1) which basically you are trying to
estimate from your modeling.

Isn't that only true if X & T are independent? (which they are not in
my case)

In your case X = 0 otherwise.

E(X) = Pr(T=1)*E(X) + Pr(T=0)*0 = p*E(X)


It would be better to use some proper notation throughout. The above is better written as the following, which
shows the role of dependence:

E(X) = Pr(T=1)*E(X|T=1) + Pr(T=0)*E(X|T=0) = p*E(X|T=1).

David Jones


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